Los Angeles Math Circle

LAMC Meetings • 2019-2020 Academic Year

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For meetings prior to Fall 2019, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPIntermediate 1A
Intermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
10/6/2019

Introduction to Gaussian integers, as well as prime and irreducible Gaussian integers





10/13/2019

Characterization of which positive integers are sums of squares



10/20/2019

We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns.

10/27/2019

We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns.

11/3/2019

Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofs

Handouts: Proofs 1
11/10/2019

Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofs

Handouts: Proofs 2
11/17/2019
11/24/2019
12/8/2019

A 2 hour long math competition against the other high school group!

1/12/2020

We introduce a new notion of distance - the taxicab metric. We investigate how geometry behaves with this new distance, and try to find similarities and differences between this and the Euclidean metric.

Handouts: Metrics 1
1/19/2020

We continue our study of metrics, this time considering more abstract examples. We discuss sequences, and we learn that with regards to sequences, the taxicab metric and the Euclidean metric are equivalent.

Handouts: Metrics 2
1/26/2020

We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension?

2/2/2020

With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers.

2/9/2020

We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins.

2/23/2020
Handouts: Probability 1
3/1/2020
Handouts: Probability 2
3/8/2020
3/15/2020
4/5/2020

Travel back in time and revisit some of the old topics from Winter 2020

Handouts: Time Travel
4/12/2020

We revisit metrics, this time with the goal of understanding fixed points.

4/19/2020

We discuss some interesting graph theory, as well as a strange application to fixed points

4/26/2020
5/3/2020
5/10/2020
5/17/2020
5/31/2020
6/7/2020